Question

A solid compound XY has $NaCl$ structure. If the radius of the cation is 100 pm, the radius of the anion $\left(Y^{-}\right)$ will be:

• A. 275.1 pm
• B. 322.5 pm
• C. 241.5 pm
• D. 165.7 pm

Answer 1

The correct option is C 241.5 pm

$NaCl$ has face centred cubic arrangement of $C{l}^{-}$ ions and $N{a}^{+}$ ions are present in the octahedral voids. Hence, for such a solid radius of cation $=0.414\times \text{radius of the anion}$
$\frac{r_{+}}{r_{-}}=0.414$
$r_{+}=0.414r_{-}$
$r_{-}=\frac{r_{+}}{0.414}=\frac{100}{0.414}=241.5\text{pm}$